Quasar parallax: A method for determining direct geometrical distances to quasars

We describe a novel method to determine direct geometrical distances to quasars that can measure the cosmological constant, Lambda, with minimal assumptions. This method is equivalent to geometric parallax, with the standard length being the size of the quasar broad emission line region (BELR) as determined from the light-travel time measurements of reverberation mapping. The effect of nonzero Lambda on angular diameter is large, 40% at z = 2, so mapping angular diameter distances versus redshift will give Lambda with (relative) ease. In principle, these measurements could be made in the UV, optical, near-infrared, or even X-ray bands. Interferometers with a resolution of 0.01 mas are needed to measure the size of the BELR in z = 2 quasars, which appear plausible given reasonable short-term extrapolations of current technology.